0.2x^2+0.1x-5.1=8

Solution for 0.2x^2+0.1x-5.1=8 equation:

0.2x^2+0.1x-5.1=8

We move all terms to the left:

0.2x^2+0.1x-5.1-(8)=0

We add all the numbers together, and all the variables

0.2x^2+0.1x-13.1=0

a = 0.2; b = 0.1; c = -13.1;
Δ = b2-4ac
Δ = 0.12-4·0.2·(-13.1)
Δ = 10.49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.1)-\sqrt{10.49}}{2*0.2}=\frac{-0.1-\sqrt{10.49}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1)+\sqrt{10.49}}{2*0.2}=\frac{-0.1+\sqrt{10.49}}{0.4}
$